The boat was struck by another vessel while moored in the Hungarian capital at about 10pm local time (8pm GMT), state news agency MTI reports.
According to MTI, there were 33 people on board when the incident happened, mainly South Korean tourists, as well as two crew.
Reuters reports 21 people, all South Korean, were still missing on Thursday morning (30 May).
The tourists were travelling with Korea’s Very Good Tour company.
The incident happened near the Hungarian parliament building, one of the city’s most popular tourist hotspots.